The minimum weakly connected dominating set problem is a classic NP-hard problem that has wide applications in various fields. This study proposes an efficient local search algorithm to solve this problem. The algorithm employs a method to construct an initial solution based on locked vertices and frequency feedback. This method ensures the inclusion of vertices that are certain or highly likely to be in the optimal solution, resulting in a high-quality initial solution. Furthermore, the study introduces a method to avoid cycling based on two-hop configuration checking, age properties, and tabu strategies. A perturbation strategy is also proposed to enable the algorithm to effectively escape from the local optimum. Additionally, effective vertex selection methods are presented to assist the algorithm in choosing vertices suitable for addition to or removal from the candidate solution by combining two scoring functions, Dscore and Nscore, with strategies for avoiding cycling. Finally, the proposed local search algorithm is evaluated on four benchmark test instances and compared with four state-of-the-art algorithms and the CPELX solver. Experimental results demonstrate that the proposed algorithm achieves better performance.